Class 9 Physics – Chapter 5: Work, Energy and Power

Introduction to Work, Energy and Power

Work, energy, and power are fundamental concepts in physics that describe how forces cause motion, how energy is transferred and transformed, and how quickly work is done.

When we push a box, lift a book, or run up stairs, we're doing work. This chapter explores the relationship between force, displacement, and energy, and how these concepts are interconnected through the principle of conservation of energy.

Key Concepts Covered

Definition and calculation of work
Different forms of energy (kinetic, potential)
Law of conservation of energy
Power and efficiency
Renewable and non-renewable energy sources
Applications of energy in daily life
Environmental impact of energy production

Important Definitions

Work: Work is said to be done when a force acts on an object and moves it through some distance. Mathematically, \( W = F \times S \).

Energy: The ability of a body to do work. The SI unit of energy is joule (J).

Kinetic Energy: The energy that a body possesses by virtue of its motion. \( E_k = \frac{1}{2}mv^2 \).

Potential Energy: The energy that a body possesses by virtue of its position or deformation. \( E_p = mgh \).

Power: The time rate of doing work. \( P = \frac{W}{t} \). The SI unit of power is watt (W).

Efficiency: The ratio of useful output energy to the total input energy, often expressed as a percentage.

Conservation of Energy: Energy cannot be created or destroyed; it may be transformed from one form to another, but the total amount of energy never changes.

Key Formulas

Work Done

\[W = F \times S\]

Where \( W \) is work, \( F \) is force, and \( S \) is displacement

Work Done at an Angle

\[W = FS \cos \theta\]

Where \( \theta \) is the angle between force and displacement

Kinetic Energy

\[E_k = \frac{1}{2}mv^2\]

Where \( m \) is mass and \( v \) is velocity

Potential Energy

\[E_p = mgh\]

Where \( m \) is mass, \( g \) is gravitational acceleration, and \( h \) is height

Power

\[P = \frac{W}{t}\]

Where \( P \) is power, \( W \) is work, and \( t \) is time

Efficiency

\[\text{Efficiency} = \frac{\text{Useful output energy}}{\text{Total input energy}} \times 100\%\]

Detailed Chapter Content

1. Work

Work is done when a force causes displacement in the direction of the force. If there is no displacement, no work is done regardless of how much force is applied.

Special cases:

When \( \theta = 0^\circ \), \( \cos 0^\circ = 1 \), so \( W = FS \) (maximum work)
When \( \theta = 90^\circ \), \( \cos 90^\circ = 0 \), so \( W = 0 \) (no work done)

2. Energy

Energy exists in many forms and can be converted from one form to another. The two basic forms of mechanical energy are:

Kinetic Energy Potential Energy Energy due to motion Energy due to position or deformation \( E_k = \frac{1}{2}mv^2 \) \( E_p = mgh \) Depends on mass and velocity Depends on mass, height, and gravity Examples: moving car, flowing water Examples: water in dam, stretched spring

3. Forms of Potential Energy

Gravitational Potential Energy: Energy due to position relative to Earth
Elastic Potential Energy: Energy stored in compressed or stretched springs
Chemical Potential Energy: Energy stored in chemicals (batteries, fuels)
Nuclear Energy: Energy stored in atomic nuclei

4. Conservation of Energy

The total energy in an isolated system remains constant. Energy can change from one form to another but cannot be created or destroyed.

Example: A falling object converts potential energy to kinetic energy, but the total mechanical energy remains constant (ignoring air resistance).

5. Energy Sources

Renewable Energy Non-renewable Energy Replaced naturally after use Depleted with continuous use Examples: solar, wind, hydro, tidal, geothermal, biomass Examples: fossil fuels (coal, oil, natural gas), nuclear Environmentally friendly Causes pollution Not going to run out Limited quantity

6. Power and Efficiency

Power measures how quickly work is done. Efficiency measures how effectively energy is converted from one form to another.

No system can have 100% efficiency due to energy losses (mainly as heat from friction).

7. Environmental Impact of Energy Production

Fossil fuels: Produce smoke, CO₂, and heat pollution
Nuclear energy: Risk of radiation leakage and waste disposal problems
Renewable sources: Generally cleaner but may have other environmental impacts
Thermal pollution: Waste energy ends up as heat, contributing to global warming

Sample Problems

Problem 1: Work Calculation

Given:

A force of 10 N is applied to move a box through a distance of 5 m in the direction of the force.

Solution:

Using the formula \( W = F \times S \):

\( W = 10 \, \text{N} \times 5 \, \text{m} = 50 \, \text{J} \)

The work done is 50 joules.

Problem 2: Kinetic Energy Comparison

Given:

A slow-moving car (mass = 1000 kg, velocity = 5 m/s) and a fast-moving motorcycle (mass = 200 kg, velocity = 20 m/s).

Solution:

Car's kinetic energy: \( E_k = \frac{1}{2} \times 1000 \times (5)^2 = 12,500 \, \text{J} \)

Motorcycle's kinetic energy: \( E_k = \frac{1}{2} \times 200 \times (20)^2 = 40,000 \, \text{J} \)

The motorcycle has more kinetic energy despite having less mass, due to its higher velocity.

Problem 3: Power Calculation

Given:

Force F₁ does 5 J of work in 10 s. Force F₂ does 3 J of work in 5 s.

Solution:

Power of F₁: \( P_1 = \frac{5}{10} = 0.5 \, \text{W} \)

Power of F₂: \( P_2 = \frac{3}{5} = 0.6 \, \text{W} \)

Force F₂ delivers more power.